document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106435>Question 106435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I want to build a dome with a cir. of 60' and the top cut off to provide a 3' dia. hole (cir.=9.24') in the top.  I would like to know the circumference of 7 additional rings besides the 2 mentioned of 60' and 9.24'.  Each positioned equadistance up the outside of the sphere.  The idea to build a geodesic dome with triangular suports between each outside ring.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77467 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-10%2C+0%2C+0%2C+10%0D%0A%2Cgrid%28+1+%29%2Ccircle%28+0%2C+0%2C+9.549+%29%2Ccircle%28-.75%2C9.519%2C.2%29%2Ccircle%28-9.549%2C0%2C.2%29%2Clocate%28-1.5%2C10%2C+2%29%2Clocate%28-10%2C.8%2C1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A circumference of 60' gives a radius of <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+2+%28pi%29+R ALIGN=MIDDLE  ALT=\"C+=+2+%28pi%29+R\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=60%2F%282+%28pi%29+%29 ALIGN=MIDDLE  ALT=\"R=60%2F%282+%28pi%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so then at C=60 ft, then<BR>\n" );
document.write( "R=9.549 feet<BR>\n" );
document.write( "The radius at the top is R=1.5 feet. <BR>\n" );
document.write( "The y dimension between the 60 ft circumference (R=9.549) ring (Point 1) and the R=1.5 ft ring (Point 2) can be calculated by finding the y dimensions of each and subtracting.<BR>\n" );
document.write( "You can do this since both points lie on the circle with radius R=9.549. <BR>\n" );
document.write( "For point 1, <BR>\n" );
document.write( "x=-9.549, y=0<BR>\n" );
document.write( "For point 2,<BR>\n" );
document.write( "x=-1.5 and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2=x%5E2%2By%5E2 ALIGN=MIDDLE  ALT=\"R%5E2=x%5E2%2By%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289.549%29%5E2=%281.5%29%5E2%2By%5E2 ALIGN=MIDDLE  ALT=\"%289.549%29%5E2=%281.5%29%5E2%2By%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=%2888.939%29 ALIGN=MIDDLE  ALT=\"y%5E2=%2888.939%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9.431 ALIGN=MIDDLE  ALT=\"y=9.431\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The difference in y is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28DELTA%29+y+=+9.431+-+0 ALIGN=MIDDLE  ALT=\"%28DELTA%29+y+=+9.431+-+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28DELTA%29+y+=+9.431 ALIGN=MIDDLE  ALT=\"%28DELTA%29+y+=+9.431\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28DELTA%29+y ALIGN=MIDDLE  ALT=\"%28DELTA%29+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > is broken up by 7 additional points into 8 equidistant spacings of 9.431/8=1.179 feet.<BR>\n" );
document.write( "We can then calculate the corresponding x values that go with the y values. <BR>\n" );
document.write( "The x values are then the radii of the 7 additional rings and we can measure the circumference. <BR>\n" );
document.write( "Let's start.<BR>\n" );
document.write( "Point 1 is at y=0, each other y will be a multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28DELTA%29+y ALIGN=MIDDLE  ALT=\"%28DELTA%29+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B3%5D=%28DELTA%29y=1.179 ALIGN=MIDDLE  ALT=\"y%5B3%5D=%28DELTA%29y=1.179\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B4%5D=2%2A%28DELTA%29y=2.358 ALIGN=MIDDLE  ALT=\"y%5B4%5D=2%2A%28DELTA%29y=2.358\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B5%5D=3%2A%28DELTA%29y=3.537 ALIGN=MIDDLE  ALT=\"y%5B5%5D=3%2A%28DELTA%29y=3.537\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B6%5D=4%2A%28DELTA%29y=4.715 ALIGN=MIDDLE  ALT=\"y%5B6%5D=4%2A%28DELTA%29y=4.715\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B7%5D=5%2A%28DELTA%29y=5.894 ALIGN=MIDDLE  ALT=\"y%5B7%5D=5%2A%28DELTA%29y=5.894\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B8%5D=6%2A%28DELTA%29y=7.073 ALIGN=MIDDLE  ALT=\"y%5B8%5D=6%2A%28DELTA%29y=7.073\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B9%5D=7%2A%28DELTA%29y=8.252 ALIGN=MIDDLE  ALT=\"y%5B9%5D=7%2A%28DELTA%29y=8.252\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The corresponding x's are calculated using <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Bn%5D%29%5E2%2B%28y%5Bn%5D%29%5E2=9.549%5E2 ALIGN=MIDDLE  ALT=\"%28x%5Bn%5D%29%5E2%2B%28y%5Bn%5D%29%5E2=9.549%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "with the results<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=9.476 ALIGN=MIDDLE  ALT=\"x%5B3%5D=9.476\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D=9.254 ALIGN=MIDDLE  ALT=\"x%5B4%5D=9.254\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B5%5D=8.870 ALIGN=MIDDLE  ALT=\"x%5B5%5D=8.870\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B6%5D=8.304 ALIGN=MIDDLE  ALT=\"x%5B6%5D=8.304\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B7%5D=7.513 ALIGN=MIDDLE  ALT=\"x%5B7%5D=7.513\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B8%5D=6.416 ALIGN=MIDDLE  ALT=\"x%5B8%5D=6.416\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B9%5D=4.806 ALIGN=MIDDLE  ALT=\"x%5B9%5D=4.806\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "These are then the radii for each of the rings and the circumference is equal to,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=2%28pi%29R%5Bn%5D=2%28pi%29x%5Bn%5D ALIGN=MIDDLE  ALT=\"C=2%28pi%29R%5Bn%5D=2%28pi%29x%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B3%5D=59.54 ALIGN=MIDDLE  ALT=\"C%5B3%5D=59.54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B4%5D=58.14 ALIGN=MIDDLE  ALT=\"C%5B4%5D=58.14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B5%5D=55.73 ALIGN=MIDDLE  ALT=\"C%5B5%5D=55.73\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B6%5D=52.17 ALIGN=MIDDLE  ALT=\"C%5B6%5D=52.17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B7%5D=47.21 ALIGN=MIDDLE  ALT=\"C%5B7%5D=47.21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B8%5D=40.31 ALIGN=MIDDLE  ALT=\"C%5B8%5D=40.31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B9%5D=30.20 ALIGN=MIDDLE  ALT=\"C%5B9%5D=30.20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-10%2C+0%2C+0%2C+10%0D%0A%2Cgrid%28+1+%29%2Ccircle%28+0%2C+0%2C+9.549+%29%2Ccircle%28-.75%2C9.519%2C.2%29%2Ccircle%28-9.549%2C0%2C.2%29%2Clocate%28-1.5%2C10%2C+2%29%2Clocate%28-10%2C.8%2C1%29%2C%0D%0Acircle%28-9.476%2C1.179%2C.2%29%2Clocate%28-9.8%2C2%2C3%29%2C%0D%0Acircle%28-9.254%2C2.358%2C.2%29%2Clocate%28-9.6%2C3.1%2C4%29%2C%0D%0Acircle%28-8.870%2C3.537%2C.2%29%2Clocate%28-9.4%2C4.0%2C5%29%2C%0D%0Acircle%28-8.304%2C4.715%2C.2%29%2Clocate%28-8.8%2C5.0%2C6%29%2C%0D%0Acircle%28-7.513%2C5.894%2C.2%29%2Clocate%28-8%2C6.4%2C7%29%2C%0D%0Acircle%28-6.416%2C7.073%2C.2%29%2Clocate%28-6.6%2C7.8%2C8%29%2C%0D%0Acircle%28-4.806%2C8.252%2C.2%29%2Clocate%28-4.7%2C8.9%2C9%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );